Probabilistic modeling of quasibrittle fracture and size effect

Progres si nstructura ldesig nrequire sprobabilisti cmodelin go fquasibrittle fracture ,whic hi stypica lo fconcrete ,fibe rcomposites ,rocks ,toughene dceramics ,se aic eand man y'hig htech 'materials .Th emos timportan tconsequenc eo fquasibrittl ebehavio ri sa deterministi c(energetic )siz eeffect ,th etheor yo fwhic hevolve dnea rth een do flas tcentury. After a review of the background, the present plenary lecture describes the recent efforts to combin eth eclassica lWeibul ltheor yo fstatistica lsiz eeffec tdu et oloca lstrengt hrandomness with the recently developed energetic theory, and also surveys various related problems, such as the probability tail structure of the stochastic finite element methods, the random scatter in fracture testing, the role of fractal nature of cracks, the reliability provisions of design codes, and the lessons from past structural catastrophes.

[1]  L. H. C. Tippett,et al.  ON THE EXTREME INDIVIDUALS AND THE RANGE OF SAMPLES TAKEN FROM A NORMAL POPULATION , 1925 .

[2]  W. Weibull,et al.  The phenomenon of rupture in solids , 1939 .

[3]  Drahomír Novák,et al.  ENERGETIC-STATISTICAL SIZE EFFECT IN QUASIBRITTLE FAILURE AT CRACK INITIATION , 2000 .

[4]  Humberto Contreras,et al.  The stochastic finite-element method , 1980 .

[5]  Rhj Ron Peerlings,et al.  Gradient enhanced damage for quasi-brittle materials , 1996 .

[6]  Alberto Carpinteri,et al.  Fractal nature of material microstructure and size effects on apparent mechanical properties , 1994 .

[7]  W. Weibull,et al.  Basic aspects of fatigue , 1956 .

[8]  Surendra P. Shah,et al.  Size-effect method for determining fracture energy and process zone size of concrete , 1990 .

[9]  A. Carpinteri.  Scaling laws and renormalization groups for strength and toughness of disordered materials , 1994 .

[10]  A. Pineau,et al.  A local criterion for cleavage fracture of a nuclear pressure vessel steel , 1983 .

[11]  Alberto Carpinteri,et al.  Multifractal scaling law for the nominal strength variation of concrete structures , 1993 .

[12]  Miguel Angel,et al.  Objective simulation of failure in heterogeneous softening solids : the use of stochastic imperfections in localisation analysis , 1999 .

[13]  Benjamin Epstein,et al.  Statistical Aspects of Fracture Problems , 1948 .

[14]  L. Sedov.  Similarity and Dimensional Methods in Mechanics , 1960 .

[15]  Ted Belytschko,et al.  Finite element methods in probabilistic mechanics , 1987 .

[16]  森山 昌彦,et al.  「確率有限要素法」(Stochastic Finite Element Method) , 1985 .

[17]  Claudio Ruggieri,et al.  A transferability model for brittle fracture including constraint and ductile tearing effects: a probabilistic approach , 1996 .

[18]  Zdeněk P. Bažant,et al.  Cohesive Crack Model with Rate-Dependent Opening and Viscoelasticity: II. Numerical Algorithm, Behavior and Size Effect , 1997 .

[19]  Masanobu Shinozuka,et al.  Response Variability of Stochastic Finite Element Systems , 1988 .

[20]  R. de Borst,et al.  Stochastic aspects of localised failure: material and boundary imperfections , 2000 .

[21]  Ek P. Ba.  Scaling of quasibrittle fracture: hypotheses of invasive and lacunar fractality, their critique and Weibull connection , 1997 .

[22]  Peter Marti,et al.  Size Effect in Double-Punch Tests on Concrete Cylinders , 1989 .

[23]  Z. Bažant,et al.  Stability of Structures: Elastic, Inelastic, Fracture, and Damage Theories , 1993 .

[24]  Zdenek P. Bazant,et al.  Size effect on diagonal shear failure of beams without stirrups , 1991 .

[25]  Drahomír Novák,et al.  PROBABILISTIC NONLOCAL THEORY FOR QUASIBRITTLE FRACTURE INITIATION AND SIZE EFFECT. II: APPLICATION , 2000 .

[26]  G. A. Webster,et al.  Weibull Stress Solutions for 2-D Cracks in elastic and Elastic-Plastic Materials , 1998 .

[27]  Tsuyoshi Takada,et al.  Weighted integral method in multi-dimensional stochastic finite element analysis , 1990 .

[28]  A. M. Freudenthal,et al.  On the statistical interpretation of fatigue tests , 1953, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[29]  Drahomír Novák,et al.  Proposal for Standard Test of Modulus of Rupture of Concrete with Its Size Dependence , 2001 .

[30]  P. Kittl,et al.  Size effect on fracture strength in the probabilistic strength of materials , 1990 .

[31]  Zdenek P. Bazant,et al.  FRACTURING TRUSS MODEL: SIZE EFFECT IN SHEAR FAILURE OF REINFORCED CONCRETE , 1997 .

[32]  Mircea Grigoriu,et al.  Reliability Analysis of Dynamic Daniels Systems with Local Load-Sharing Rule , 1990 .

[33]  Pol D. Spanos,et al.  Probabilistic engineering mechanics , 1992 .

[34]  Robert O. Ritchie,et al.  A Statistical RKR Fracture Model for the Brittle Fracture of Functionally Graded Materials , 1999 .

[35]  G. I. Barenblatt.  Scaling: Self-similarity and intermediate asymptotics , 1996 .

[36]  B. Brookes,et al.  Statistical Theory of Extreme Values and Some Practical Applications , 1955, The Mathematical Gazette.

[37]  George N Frantziskonis,et al.  Stochastic modeling of heterogeneous materials – A process for the analysis and evaluation of alternative formulations , 1998 .

[38]  J. Carmeliet,et al.  On Stochastic Descriptions for Damage Evolution in Quasi-Brittle Materials , 1994 .

[39]  Masanori Izumi,et al.  A stochastic theory for concrete fracture , 1977 .

[40]  Hinch.  Perturbation Methods , 1991 .

[41]  Z. Bažant,et al.  SIZE EFFECT IN TENSILE AND COMPRESSION FRACTURE OF CONCRETE STRUCTURES : COMPUTATIONAL MODELING AND DESIGN , 2022 .

[42]  Zdeněk P. Bažant,et al.  Fracture energy release and size effect in borehole breakout , 1993 .

[43]  Anthony G. Evans,et al.  A statistical model of brittle fracture by transgranular cleavage , 1986 .

[44]  Masanobu Shinozuka,et al.  Weighted Integral Method. II: Response Variability and Reliability , 1991 .

[45]  Zdeněk P. Bažant,et al.  Size effect in concrete structures , 1994 .

[46]  Zdeněk P. Bažant,et al.  Size effect on compression strength of fiber composites failing by kink band propagation , 1999 .

[47]  Dan M. Frangopol,et al.  Size Effect Hidden in Excessive Dead Load Factor , 2002 .

[48]  Shinozuka,et al.  Statistical and fractal aspects of size effect in quasibrittle structures : Conspectus of recent results , 2022 .

[49]  G. I. Barenblatt,et al.  Similarity, Self-Similarity and Intermediate Asymptotics , 1979 .

[50]  S. Orszag,et al.  Advanced Mathematical Methods For Scientists And Engineers , 1979 .

[51]  A. Hillerborg,et al.  Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements , 1976 .

[52]  Hikaru Akiyama,et al.  EXPERIMENTAL STUDIES ON THE SHEAR STRENGTH OF LARGE REINFORCED CONCRETE BEAMS UNDER UNIFORMLY DISTRIBUTED LOAD , 1984 .

[53]  Ek P. Ba.  Scaling of quasibrittle fracture: asymptotic analysis , 1997 .

[54]  G. Schuëller.  A state-of-the-art report on computational stochastic mechanics , 1997 .

[55]  W. Weibull.  A Statistical Distribution Function of Wide Applicability , 1951 .

[56]  Z. Bažant,et al.  Strain Softening with Creep and Exponential Algorithm , 1985 .

[57]  G. I. Schuëller,et al.  A complex study on the reliability assessment of the containment of a PWR Parts I–III☆ , 1978 .

[58]  Z. Bažant.  Size Effect in Blunt Fracture: Concrete, Rock, Metal , 1984 .

[59]  Bhushan Lal Karihaloo,et al.  Determination of specimen-size independent fracture toughness of plain concrete , 1986 .

[60]  Mohammad Taghi Kazemi,et al.  Size Effect in Fracture of Ceramics and Its Use To Determine Fracture Energy and Effective Process Zone Length , 1990 .

[61]  Zdenek P. Bazant,et al.  Size effect in penetration of sea ice plate with part-through cracks. I : Theory , 1998 .

[62]  Anthony G. Evans,et al.  A General Approach for the Statistical Analysis of Multiaxial Fracture , 1978 .

[63]  J. C. Walraven,et al.  Size effects : Their nature and their recognition in building codes , 1995 .

[64]  Zdenek P. Bazant,et al.  Instability, Ductility, and Size Effect in Strain-Softening Concrete , 1978 .

[65]  Z. Bažant,et al.  Determination of Fracture Energy from Size Effect and Brittleness Number , 1987 .

[66]  R. Rackwitz,et al.  On predictive distribution functions for the three asymptotic extreme value distributions , 1992 .

[67]  Zdenek P. Bazant,et al.  Size Effect and Fracture Characteristics of Composite Laminates , 1996 .

[68]  V. V. Bolotin.  Statistical Methods in Structural Mechanics , 1969 .

[69]  Drahomír Novák,et al.  PROBABILISTIC NONLOCAL THEORY FOR QUASIBRITTLE FRACTURE INITIATION AND SIZE EFFECT. I: THEORY , 2000 .

[70]  K. Trustrum,et al.  Statistical approach to brittle fracture , 1977 .

[71]  Drahomír Novák,et al.  Nonlocal Weibull theory and size effect in failures at fracture initiation , 2001 .

[72]  Vimal Singh,et al.  Perturbation methods , 1991 .

[73]  Z. Bažant,et al.  Fracture and Size Effect in Concrete and Other Quasibrittle Materials , 1997 .

[74]  Z. Bažant.  FRACTURE MECHANICS OF CONCRETE STRUCTURES , 1992 .

[75]  B. Gnedenko.  Sur La Distribution Limite Du Terme Maximum D'Une Serie Aleatoire , 1943 .

[76]  Zdenek P. Bazant,et al.  Scaling of Structural Failure , 1997 .

[77]  Zden Ek,et al.  Concrete Fracture Models: Testing and Practice , 2022 .

[78]  김동수,et al.  콘크리트 파괴에너지 결정에 관한 연구 = Determination of the fracture energy of concrete , 1986 .

[79]  Zdenek P. Bazant,et al.  Scaling laws in mechanics of failure , 1993 .

[80]  Isaac M Daniel,et al.  Analysis of Fracture Probabilities in Nonuniformly Stressed Brittle Materials , 1964 .

[81]  Jan Carmeliet,et al.  Probabilistic Nonlocal Damage Model for Continua with Random Field Properties , 1994 .

[82]  E. J. Gumbel,et al.  Statistics of Extremes. , 1960 .

[83]  P. Kittl,et al.  Weivull's fracture statistics, or probabilistic strength of materials: state of the art , 1988 .

[84]  Denis Breysse,et al.  A probabilistic formulation of the damage evolution law , 1990 .

[85]  Surendra P. Shah,et al.  Two Parameter Fracture Model for Concrete , 1985 .

[86]  Z. Bažant,et al.  Scaling of quasibrittle fracture: asymptotic analysis , 1997 .

[87]  J. Glucklich.  Fracture of Plain Concrete , 1963 .

[88]  Anthony G. Evans,et al.  Statistical aspects of cleavage fracture in steel , 1983 .

[89]  S. Leigh Phoenix,et al.  Stochastic strength and fatigue of fiber bundles , 1978, International Journal of Fracture.

[90]  P. F. Walsh.  Crack initiation in plain concrete , 1976 .

[91]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[92]  Zdeněk P. Bažant,et al.  Large-scale thermal bending fracture of sea ice plates , 1992 .

[93]  R. Fisher,et al.  Limiting forms of the frequency distribution of the largest or smallest member of a sample , 1928, Mathematical Proceedings of the Cambridge Philosophical Society.

[94]  J. R. Ockendon,et al.  SIMILARITY, SELF‐SIMILARITY AND INTERMEDIATE ASYMPTOTICS , 1980 .

[95]  L. Vinci.  The notebooks of Leonardo da Vinci. , 1952 .

[96]  Joost Walravena,et al.  Size effects in short beams loaded in shear , 1994 .

[97]  M. Fréchet.  Sur la loi de probabilité de l'écart maximum , 1928 .

[98]  ZdĚnk P. BaŽant,et al.  Scaling of quasibrittle fracture: hypotheses of invasive and lacunar fractality, their critique and Weibull connection , 1997 .

[99]  Gilles Pijaudier-Cabot,et al.  Nonlocal Weibull theory and size effect in failures at fracture initiation , 2022 .

[100]  E. Williams,et al.  Some observations of Leonardo, Galileo, Mariotte and others relative to size effect , 1957 .

[101]  Yiu-Wing Mai,et al.  Crack Stability and Toughness Characteristics in Brittle Materials , 1986 .

[102]  A. M. Freudenthal,et al.  Physical and Statistical Aspects of Fatigue , 1956 .